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Math Help - global existence and uniqueness

  1. #1
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    global existence and uniqueness

    Show that for any x0 in R there exists a unique global solution x: R->R of the initial value problem
    x’(t) = (x(t)2 + t)sin(x(t))
    x(0) = x0

    could anyone please help me to do this question ?? ,, ,
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  2. #2
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    Quote Originally Posted by jin_nzzang View Post
    Show that for any x0 in R there exists a unique global solution x: R->R of the initial value problem
    x’(t) = (x(t)2 + t)sin(x(t))
    x(0) = x0

    could anyone please help me to do this question ?? ,, ,
    Picard?Lindelöf theorem - Wikipedia, the free encyclopedia

    The big part is to prove that f(t,x)=(x^2+t)sin(x) is Lipschitz continuous in y, uniformly continuous in t. For that, the mean value theorem would be helpful.
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  3. #3
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    The difficulty is that "Picard-Lindelof" only shows that the solution exists on some interval about the "initial" point, not that the solution is global.
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